I suspect a really good place to mine for information is the Lichess pgn downloads.https://database.lichess.org/
Turn the PGN games into EPD and then count the piece signatures you see.
You would not need to save the PGN or EPD from the bz2 archives.
Just pipe the decompression operation to a transform PGN to EPD tool like pgn2fen and then pipe the output of pgn2fen to a signature counting tool.
I think the last one would have to be written but it should not be terribly difficult. Program filter_counter would:
0) For each PGN file
1) Toss out all EPD strings that do not have exactly 7 chessmen.
2) Examine the board to create a signature in the same format as the EGTB file names
3) Bump the count for the slot that matches the signature.
4) When the PGN file is exhausted, write the collected statistics to a database.

Since every possible signature is known, you could make a perfect hash and it should be really fast.

I know you have a ton of FICS data, but that stuff is awfully low quality.
Lichess is probably some better.

You could go with a smaller set of data like TWIC or use computer data like CCRL and/or CEGT.
It would be interesting to see if computer verses computer data has a different signature profile than human verses human games.

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Only one 7-men position is counted per game if present. Types KRPPvKRp and KRpvKRPP are just considered as KRPPvKRp under type column.
If a game has KRPPvKRP and another game has KRpvKRPP then the count for KRPPvKRP will be 2. The same is applied for other types.
Reading the table, KRPPvKRP has comp count of 1168 pos with an equivalent 15.24% for comp alone while it has a human equivalent of 553 counts with 33.01% for human alone.

Only one 7-men position is counted per game if present. Types KRPPvKRp and KRpvKRPP are just considered as KRPPvKRp under type column.
If a game has KRPPvKRP and another game has KRpvKRPP then the count for KRPPvKRP will be 2. The same is applied for other types.
Reading the table, KRPPvKRP has comp count of 1168 pos with an equivalent 15.24% for comp alone while it has a human equivalent of 553 counts with 33.01% for human alone.